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<h1 align=center> Grommer inequalities
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Let 
$$-\frac{\Xi'}{\Xi}(t)=s_1+s_2t+s_3t^2+\dots.$$
Let $M_n$ be the matrix whose $i,j$ entry is $s_{i+j}$. 
J. Grommer (J. Reine Angew. Math.  144 (1914), 114--165) proved that necessary and sufficient conditions for the truth of the Riemann Hypothesis are that
$$\det M_n>0 $$
for all $n\ge 1.$

See also the paper of R. Alter [\begin{rawhtml}MR 36 \#1399\end{rawhtml}].
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Back to the 
<a href="http://www.aimath.org/WWN/rh/"> main index</a> 
for The Riemann Hypothesis.
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